Whether the order of the placements matters: Yoma 61a
Placement on the limbs of the right side of the body: Yevamot 104a
Specific finger (thumb) to use for placement: Ketuvot 5b
Use of the left hand for these rites: Zevachim 24b
Need one bring all of the oil when he brings the asham: Zevachim 44a-b
Textual source for the right of the kohanim to the oil as a gift to the kohanim: Zevachim 44b

What-Ifs

A thumb-less or toe-less metzora: Yoma 61b
Whether all of the placements of oil are requirements: Zevachim 40a, 44a
Whether the placement of the remaining oil on his head is a requirement: Zevachim 6b
At what point is one permitted to use the remaining oil for himself: Zevachim 44a-b
Is pigul intent while bringing the metzora's korban asham significant for the oil, if the oil is not directly rendered permissible by the asham itself: Zevachim 42b-43b, 44a-b

Other

The metzora gains atonement by having the oil placed on his head: Zevachim 6b
Do we consider the blood of the metzora's korban asham a matir for personal use of the oil remnants, since the oil may not be used until the asham's service is complete - or not, since the oil may be brought at a later date: Zevachim 43a, 44a-b